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Dec 2000

Volume 68, Issue 12, pp. 1073-1160

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Experiments in statistical mechanics

Jeffrey J. Prentis

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1073 | Cited 8 times

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We present experiments designed to illustrate the basic concepts of statistical mechanics using a gas of “motorized molecules.” Two molecular motion machines are constructed. The pressure fluctuation machine (mechanical interaction simulator) is a working model of two gases separated by a movable piston. The Boltzmann machine (canonical simulator) is a working model of a two-level quantum system in a temperature bath. Dynamical probabilities (fraction of time) are measured using mechanical devices, such as stop watches and motion sensors. Statistical probabilities (fraction of states) are calculated using physical statistics, such as microcanonical and canonical statistics. The experiments enable one to quantitatively test the fundamental principles of statistical mechanics, including the fundamental postulate, the ergodic hypothesis, and the statistics of Boltzmann. © 2000 American Association of Physics Teachers.
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01.50.My Demonstration experiments and apparatus
05.20.-y Classical statistical mechanics
05.30.-d Quantum statistical mechanics

Conducting rod on the axis of a charged ring: The Kelvin water drop generator

Gorazd Planinšič and Tomaž Prosen

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1084

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The problem of calculating the induced surface charge density along the finite length grounded conducting rod placed on the axis of the charged ring is solved numerically and compared with the experimental results. Two cases are considered in the theoretical treatment: the ring connected to a constant potential and the ring carrying a constant charge. The problem is related to the optimization of the Kelvin water drop electrostatic generator. A simple experiment is presented which gives reliable measurements of the induced charge density at the end of the conducting rod. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
41.20.Cv Electrostatics; Poisson and Laplace equations, boundary-value problems
73.40.-c Electronic transport in interface structures

Insight into entropy

Daniel F. Styer

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1090 | Cited 16 times

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What is the qualitative character of entropy? Several examples from statistical mechanics (including liquid crystal reentrant phases, two different lattice gas models, and the game of poker) demonstrate facets of this difficult question and point toward an answer. The common answer of “entropy as disorder” is regarded here as inadequate. An alternative but equally problematic analogy is “entropy as freedom.” Neither simile is perfect, but if both are used cautiously and not too literally, then the combination provides considerable insight. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
05.70.Ce Thermodynamic functions and equations of state
51.30.+i Thermodynamic properties, equations of state
65.20.-w Thermal properties of liquids
65.40.gd Entropy

Using great circles to understand motion on a rotating sphere

D. H. McIntyre

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1097 | Cited 2 times

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Motion observed in a rotating frame of reference is generally explained by invoking inertial forces. While this approach simplifies some problems, there is often little physical insight into the motion, in particular into the effects of the Coriolis force. To aid in the understanding of three-dimensional inertial forces, motion on a rotating sphere is considered from the points of view of an inertial observer and of an observer fixed on the sphere. The inertial observer observes the motion to be along a great circle fixed in the inertial frame, in analogy with simple straight-line motion in the two-dimensional case. This simple “straight-line” viewpoint of the inertial observer is reconciled qualitatively and quantitatively with the view of the rotating observer that requires inertial forces in order to account for the motion. Through a succession of simple examples, the Coriolis and centrifugal effects are isolated and illustrated, as well as effects due to the curvilinear nature of motion on a sphere. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
45.10.-b Computational methods in classical mechanics
45.05.+x General theory of classical mechanics of discrete systems

Noninertial trajectories on a fast rotating planet

Antoni Amengual

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1106

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The trajectory of a particle thrown horizontally on the surface of a planet rotating at an arbitrary speed, as viewed by an observer on the planet, is calculated numerically and is subsequently compared to the trivially calculated trajectory viewed by an inertial observer. This provides an excellent example when motion in noninertial frames is explained in a mechanics course. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
45.50.-j Dynamics and kinematics of a particle and a system of particles

The self-force and radiation reaction

F. Rohrlich

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1109 | Cited 17 times

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In view of the confusion in the literature, the nomenclature of “self-force” and “radiation reaction” is clarified. The difference in their physical meaning and their characteristic form permits one to obtain the total rate of radiation emission (both its momentum rate and its energy rate) from knowledge of the self-force. This can be done without knowledge of the asymptotic form of the radiation field. The electromagnetic case is the main topic, but the method is also applied to the emission of gravitational radiation in the linear approximation to general relativity. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.50.De Classical electromagnetism, Maxwell equations
04.30.-w Gravitational waves
04.20.-q Classical general relativity
12.20.Ds Specific calculations

Two-particle Schrödinger equation animations of wave packet–wave packet scattering

Jon J. V. Maestri, Rubin H. Landau, and Manuel J. Páez

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1113 | Cited 5 times

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A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schrödinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the coordinates of each particle, arbitrary initial and boundary conditions, and multidimensional equations. Plots and animations are given here and on the World Wide Web of the scattering of two wave packet in one dimension. © 2000 American Association of Physics Teachers.
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01.50.ht Instructional computer use
03.65.Ge Solutions of wave equations: bound states

Mirage mirror on the wall

T. Kosa and P. Palffy-Muhoray

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1120 | Cited 3 times

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We discuss mirages formed near a sun-heated wall, and consider the underlying physics. The temperature and refractive index variations in air near the wall are estimated, and a simple approximate picture of ray propagation is presented. Estimates of the thermal decay length and ray curvature are compared with experimental observations. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
42.25.Gy Edge and boundary effects; reflection and refraction
42.68.-w Atmospheric and ocean optics

Relativistically expanding spherical emitters

Erik Eriksen and Øyvind Grøn

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1123 | Cited 3 times

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We demonstrate several relativistic effects associated with expanding spherical sources of light. We show that if the surface lights up for say a month, it may be seen for a few seconds only if it expands sufficiently fast. Also it is demonstrated how the observed properties of the light source are modified by aberration and the Doppler effect. The apparent luminosity as a function of time is calculated and shown graphically. Modifications due to the motion of the light source away from the observer are calculated. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.30.+p Special relativity
42.72.-g Optical sources and standards

Classical and quantum mechanics of a particle on a rotating loop

Sayan Kar and Avinash Khare

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1128 | Cited 1 time

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A toy problem of a charged particle in a uniform magnetic field, constrained to move on a vertical rotating loop, is analyzed. After a short review of the model, we move on to its quantum mechanics. We first obtain some exact solutions of the corresponding Schrödinger equation. Thereafter, introducing the notion of instantons and bounces, we explicitly obtain such solutions in this problem. Finally, we delineate briefly the connection of this toy model with some models in field theory and statistical mechanics and mention possible extensions. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
41.20.-q Applied classical electromagnetism
03.65.Ge Solutions of wave equations: bound states

A Hamiltonian decomposition technique for improving the convergence of perturbation series

Harry A. Mavromatis

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1134

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A simple, one-parameter Hamiltonian decomposition is discussed that modifies the convergence rate of perturbation expansions and converts diverging into converging series. Two upper bound expressions are used to monitor the resulting series. The x2 and x4 potentials are studied as illustrations of this technique. © 2000 American Association of Physics Teachers.
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01.50.-i Educational aids
03.65.Ge Solutions of wave equations: bound states

On the sound field radiated by a tuning fork

Daniel A. Russell

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1139 | Cited 4 times

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When a sounding tuning fork is brought close to the ear, and rotated about its long axis, four distinct maxima and minima are heard. However, when the same tuning fork is rotated while being held at arm’s length from the ear only two maxima and minima are heard. Misconceptions concerning this phenomenon are addressed and the fundamental mode of the fork is described in terms of a linear quadrupole source. Measured directivity patterns in the near field and far field of several forks agree very well with theoretical predictions for a linear quadrupole. Other modes of vibration are shown to radiate as dipole and lateral quadrupole sources. © 2000 American Association of Physics Teachers.
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01.50.My Demonstration experiments and apparatus
43.40.Cw Vibrations of strings, rods, and beams

Measurement of group velocity dispersion using white light interferometry: A teaching laboratory experiment

I. G. Cormack, F. Baumann, and D. T. Reid

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1146 | Cited 3 times

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A teaching laboratory experiment is described which uses a basic Michelson interferometer arrangement to make fast and accurate measurements of the group velocity dispersion of an optical material using a method based on recording white-light fringes. We present a brief analysis of the theory behind the technique and describe two example measurements, one of the material dispersion of a KTP crystal and another of the reflectivity dispersion of a silver-coated mirror. Details are also given of our implementation of the data analysis using the MATLAB programming environment © 2000 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
42.25.Bs Wave propagation, transmission and absorption
07.60.Ly Interferometers
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Comment on “A single equation for finite rectangular well energy eigenvalues,” by B. Cameron Reed [Am. J. Phys. 58 (5), 503–504 (1990)]

Harry A. Mavromatis

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1151 | Cited 2 times

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Abstract Unavailable
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01.50.-i Educational aids
03.65.Fd Algebraic methods
03.65.Ge Solutions of wave equations: bound states
02.10.Ud Linear algebra
02.10.Xm Multilinear algebra

Tension loss along a string

Rod Cross

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1152

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Abstract Unavailable
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01.50.-i Educational aids
45.05.+x General theory of classical mechanics of discrete systems
46.55.+d Tribology and mechanical contacts
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An experiment for measuring the low temperature vapor line of water

S. Velasco, J. Faro, and F. L. Román

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1154 | Cited 1 time

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A simple and low cost, but accurate, method to measure the vapor pressure curve of water below the normal boiling temperature is described. The apparatus uses the expansion power of hot air and steam. The vapor pressure is calculated by applying the ideal gas law, some elementary hydrostatics, and taking into account the water expansivity. © 2000 American Association of Physics Teachers.
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01.50.Pa Laboratory experiments and apparatus
51.30.+i Thermodynamic properties, equations of state
62.10.+s Mechanical properties of liquids
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Classical and Statistical Thermodynamics

Ashley H. Carter, Author and Daniel F. Styer, Reviewer

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1158

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Abstract Unavailable
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01.30.mp Textbooks for undergraduates

Introduction to Mathematical Physiology and Biology, 2nd ed.

J. Mazumdar, Author and Peter B. Kahn, Reviewer

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1159

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Abstract Unavailable
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01.30.Vv Book reviews

Atmospheric Thermodynamics

Craig F. Bohren, Author, Bruce A. Albrecht, Author, and Daniel V. Schroeder, Reviewer

American Journal of Physics -- December 2000 -- Volume 68, Issue 12, pp. 1159

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Abstract Unavailable
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01.30.Vv Book reviews
92.60.-e Properties and dynamics of the atmosphere; meteorology
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